1. Field of the invention
The present invention relates generally to a novel apparatus which provides real time compensation for geometric and thermal errors in positioning of computer numerically controlled machine tools, coordinate measuring machines (CMMs) robots, assembly systems, and the like, and to an improved method for modeling geometric and thermal errors which is useful in real time control of such an apparatus.
2. Background Discussion
With ever increasing demand for part quality and tight tolerances in machining, it is required that machine tools be accurate and repeatable within desired tolerance limits over the entire machining volume, and in a wide variety of operating conditions. However, in practice, machine tool manufacturer specified accuracies and repeatability are not achieved under operating conditions, due to a wide variety of errors induced in the machine tool by virtue of its geometry and assembly, thermal expansion of the machine components and the process itself. These errors in general, are not within acceptable limits and need to be eliminated or reduced to achieve the desired part dimensional accuracy. In order to eliminate or reduce or compensate for these errors, it is necessary to characterize the machine, understand the process and evaluate the performance of the machine in a real machining environment.
Thermally induced error is a major source of machine tool inaccuracy. After conducting an extensive study, Peklenik remarked that thermal errors could contribute as much as 70% of the machining error. These thermally induced errors arise due to non-uniform heat generation within the machine structure, resulting in growth and tilt of the spindle and the various structural components. The heat dissipated from motors, bearings, cutting process and other heat generating components are also always unevenly distributed within the machine structure. These, together with the effects of ambient temperature changes and cutting coolant temperature changes, cause structural distortions of the machine tool. These temperature effects are in part inherent in cutting and movement operations, but in part occur because heat sources, such as motors, slides, and the machining operation itself have not been given careful consideration at the machine design stage, even though it is known that a design will generate temperature gradients during the operation of a machine. It is these temperature gradients that cause "thermal growth" in machine components.
Conventionally, this thermal growth is controlled through the use of coolants. It is not uncommon to install chillers on machine tools to precisely control the temperature of coolants. These accessories contribute to the low reliability and low up time of the machining process.
There are two methods that are commonly used in reducing thermally induced errors on machine tools: error avoidance and error compensation.
Error avoidance techniques are often implemented at the machine-design stage. These include designs to minimize the effects of heat generation within the machine structure and control the gradient of and change in environmentally encountered temperatures. For example, J. B. Bryan of Lawrence Livermore Laboratory was successful in achieving thermal stability by immersing the whole machine in a temperature-controlled "oil bath," as reported in "Technology of Machine Tools," UCRL Vol. 5, 1980. However, this method is very expensive and is thus impractical for production machines. A more practical method implemented by some machine-tool builders on expensive machines makes use of a temperature-controlled oil shower applied around the spindle area where the major thermal growth is typically found. In general, this method can help reduce the thermal growth error by as much as 50%. Of course the cost of constructing and operating the machine is increased.
Early research work in error compensation was primarily directed to direct measurement techniques, as described for example by Goodhead et al, "Automatic Detection of and Compensation for Alignment Errors in Machine Tool Slideways" Proceedings of 18.sup.th MTDR Conference, 1977, and Bryan et al., "Design of a New Error-Corrected Coordinate Measuring Machine," Precision Engineering, Vol. 1, 1979. However, with these techniques very sensitive measurement instruments must be attached to the machine. In a high volume production environment, maintenance of these instruments presents considerable difficulties for plant personnel. Current practice in manufacturing precision parts often involves compensation for various errors through periodic gaging of parts. Production is interrupted and manual compensating offsets are input to the controller. Also, additional production costs are introduced due to requirement of initial warm up cycles without cutting parts, and utilization of chillers for temperature controlled coolants.
More sophisticated error compensation techniques have been proposed, based on a knowledge of the thermal growth characteristics of the machine and use this "thermal model" in real-time to predict the thermal growth. A digital processor utilizes this model to calculate the error information which is then sent to the machine's CNC controller to compensate for the sensed error. This error information is often in the form of tool offset commands.
By using multiple thermal sensors to measure actual temperatures of major heat sources, and sensors to measure thermal growth (in the X-, Y- and Z-axis directions, and in pitch and yaw), a computer-controlled modeling system will collect and store the data while the machine spindle is running. After enough data is collected, the system will establish a thermal model by analyzing the correlation between the temperatures and the thermal growth of each axis of the machine. As soon as the performance of the model is verified, the model can be used in real-time to predict the thermal growths of the machine by using only actual temperature information. See Donmez et al., "A Real Time Error Compensation System for a Computerized Numerical Control Turning Center," Proceedings of the IEEE International Conference on Robotics and Automation, San Francisco, April 1986, and Donmez et al., "A General Methodology for Maching Tool Accuracy Enhancement by Error Compensation," Precision Engineering, Vol. 8, No. 4, October 1986.
Real time error compensation techniques using modeling have attracted the interest of machine tool manufacturers and users. Recent research on thermal error compensation conducted by F. Rudder and A. Donmez of NIST involved the establishment of a real-time geometric/thermal (G-T) model to characterize the thermal behavior of a vertical spindle machining center and a turning center. The geometric error data at various thermal states of the machine conditions were acquired and used to build the G-T model. This study was reported in "Progress Report for the Quality in Automation Project for FY 90," National Institute of Standards and Technology, March 1991.
These methods viewed a machine tool, fixture and workpiece system as a chain of linkages of rigid bodies. This work is based on spatial relations between these linkages using homogeneous coordinate transformation matrices. See R. P. Paul, "Robot Manipulators: Mathematics, Programming, and Control" MIT Press 1981. In the course of machine characterization, with machine positioning and dry cycling tests geometric/thermal errors and models are derived for each element of the machine tool linkage. Then utilizing the homogeneous transformations the total error for the tool tip, relative to workpiece, is established and is compensated for during machining cycles. Laboratory tests suggest that this technique may be highly effective in reduction of machine tool errors. However, in practice the machine characterization takes too long and is not suitable for a high volume production environment, where a major machine crash or a spindle rebuild may necessitate a full or partial recharacterization.
J. S. Chen and J. Ni of the University of Michigan (UM) developed a time-variant volumetric error model which synthesizes both the geometric and thermal errors of a machining center, as reported in "Real Time Compensation for Time Variant Volumetric Error on a Machining Center," Journal of Engineering for Industry, Vol. 115, pp. 472-479, 1993. A 21-parameter kinematic model was used to establish the geometric model of the machine. An 11 parameter thermal growth model was used to establish the spindle growth parallel to the primary axes of the machine. All together, a 32 parameter G-T model was established. In both cases, tests were conducted in a laboratory environment under dry, no load conditions. A laser interferometer system was used for the 21 geometric parameter measurements, and a combination of laser and capacitance measurements were used for the 11 parameter thermal growth measurements. The models took 2 to 6 months to establish, far too long to be practical in industry. The accuracy improvement was about 90% for simple warm-up and cool-down cycles of the machine. Thus, the conventional approaches adopted for machinery geometric and thermal error characterization are extremely time consuming.
There were also early attempts to model the entire machine tool structure utilizing the Finite Element Analysis (FEA) approach. In these analytical approaches, it is assumed that the machine structure is homogeneous and that the heat dissipation throughout the structure follows the laws of thermal conductivity. These assumptions are then used to establish the model. However, the boundary conditions of two mating surfaces, which often greatly affect the predicted thermal transitivity, are very difficult to estimate with good accuracy, as can be seen in "Analysis of Thermal Deformation of Machine Tool Structure and its Application," MTDR Conference Proceedings, Vol. 17, 1976. In addition, it is also difficult to estimate the amount of heat generated and dissipated without making actual measurements on the machine. The lack of precise knowledge of the many boundary conditions and the difficulties associated with heat dissipation factors tend to produce inaccurate results.
The prior art models were based on machine positioning variance measurements at particular measured ambient temperature values, and did not use global measurement techniques or wet modeling techniques.
Thus, none of the prior approaches to modeling thermal and geometric errors have been entirely satisfactory, and no robust, effective system has been made available for real time correction of geometric and positioning errors in an industrial setting.